Ocular optical system

ABSTRACT

An ocular optical system includes a first lens element, a second lens element, and a third lens element from an eye-side to a display-side in order along an optical axis. The first lens element, the second lens element, and the third lens element each include an eye-side surface and a display-side surface. The first lens element has refracting power. The display-side surface of the second lens element has a convex portion in a vicinity of the optical axis. The third lens element has refracting power. The ocular optical system satisfies: T3/G23≤4.3; and G3D/T3≤3.51, where T3 is a thickness of the third lens element along the optical axis, G23 is an air gap from the second lens element to the third lens element along the optical axis, and G3D is a distance from the third lens element to the display screen along the optical axis.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the priority benefit of China application serialno. 201611028369.9, filed on Nov. 18, 2016. The entirety of theabove-mentioned patent application is hereby incorporated by referenceherein and made a part of this specification.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The invention relates to an optical system, and particularly, to anocular optical system.

2. Description of Related Art

Virtual Reality (VR) refers to computer technologies used for simulatingand generating a three-dimensional virtual world, which enablesimmersive simulation for users by providing simulations pertaining tovisual sensation, auditory sensation and other sensations to users. Thecurrently existing VR devices are mainly focused on visual experiences.Binocular parallax of human eyes is simulated by separated images withtwo slightly different perspectives corresponding to the left and righteyes to achieve a stereo vision. In order to reduce the volume of the VRdevice so users can receive a magnified visual sensation from a smallerdisplay screen, an ocular optical system with magnifying capability isnow one of major topics in research and development for VR.

Because a half apparent field of view is smaller in the existing ocularoptical system, an observer may experience narrow vision, low resolutionand even aberrations so serious that an aberration compensation must beperformed on the display screen before presentation. Accordingly, how toincrease the half apparent field of view and enhance the imaging qualitybecomes one of issues to be addressed.

SUMMARY OF THE INVENTION

The invention is directed to an ocular optical system, which is capableof shortening a system length without sacrificing a favorable imagingquality and a large half apparent field of view.

An embodiment of the invention proposes an ocular optical system forimaging of imaging rays entering an eye of an observer via the ocularoptical system from a display screen. A side facing towards the eye isan eye-side, and a side facing towards the display screen is adisplay-side. The ocular optical system includes a first lens element, asecond lens element, and a third lens element from the eye-side to thedisplay-side in order along an optical axis. The first lens element, thesecond lens element, and the third lens element each include an eye-sidesurface and a display-side surface. The first lens element hasrefracting power. The display-side surface of the second lens elementhas a convex portion in a vicinity of the optical axis. The third lenselement has refracting power. The ocular optical system satisfies:T3/G23≤4.3; and G3D/T3≤3.51, where T3 is a thickness of the third lenselement along the optical axis, G23 is an air gap from the second lenselement to the third lens element along the optical axis, and G3D is adistance from the third lens element to the display screen along theoptical axis.

An embodiment of the invention proposes an ocular optical system forimaging of imaging rays entering an eye of an observer via the ocularoptical system from a display screen. A side facing towards the eye isan eye-side, and a side facing towards the display screen is adisplay-side. The ocular optical system includes a first lens element, asecond lens element, and a third lens element from the eye-side to thedisplay-side in order along an optical axis. The first lens element, thesecond lens element, and the third lens element each include an eye-sidesurface and a display-side surface. The first lens element hasrefracting power. The display-side surface of the second lens elementhas a convex portion in a vicinity of a periphery of the second lenselement. The third lens element has refracting power. The ocular opticalsystem satisfies: T3/G23≤4.3; and G3D/T3≤3.51, where T3 is a thicknessof the third lens element along the optical axis, G23 is an air gap fromthe second lens element to the third lens element along the opticalaxis, and G3D is a distance from the third lens element to the displayscreen along the optical axis.

An embodiment of the invention proposes an ocular optical system forimaging of imaging rays entering an eye of an observer via the ocularoptical system from a display screen. A side facing towards the eye isan eye-side, and a side facing towards the display screen is adisplay-side. The ocular optical system includes a first lens element, asecond lens element, and a third lens element from the eye-side to thedisplay-side in order along an optical axis. The first lens element, thesecond lens element, and the third lens element each include an eye-sidesurface and a display-side surface. The first lens element hasrefracting power. The eye-side surface of the second lens element has aconvex portion in a vicinity of the optical axis. The eye-side surfaceof the third lens element has a concave portion in a vicinity of aperiphery of the third lens element. The ocular optical systemsatisfies: T3/G23≤4.3; and G3D/T3≤3.51, where T3 is a thickness of thethird lens element along the optical axis, G23 is an air gap from thesecond lens element to the third lens element along the optical axis,and G3D is a distance from the third lens element to the display screenalong the optical axis.

Based on the above, in the embodiments of the invention, the ocularoptical system can provide the following advantageous effects. Withdesign and arrangement of the lens elements in terms of surface shapesand refracting powers as well as design of optical parameters, theocular optical system can include optical properties for overcoming theaberrations and provide the favorable imaging quality and the largeapparent field of view, given that the system length is shorten.

To make the above features and advantages of the invention morecomprehensible, several embodiments accompanied with drawings aredescribed in detail as follows.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the invention, and are incorporated in and constitute apart of this specification. The drawings illustrate embodiments of theinvention and, together with the description, serve to explain theprinciples of the invention.

FIG. 1 is a schematic view illustrating an ocular optical system.

FIG. 2 is a schematic view illustrating a surface structure of a lenselement.

FIG. 3 is a schematic view illustrating a concave and convex surfacestructure of a lens element and a ray focal point.

FIG. 4 is a schematic view illustrating a surface structure of a lenselement according to a first example.

FIG. 5 is a schematic view illustrating a surface structure of a lenselement according to a second example.

FIG. 6 is a schematic view illustrating a surface structure of a lenselement according to a third example.

FIG. 7 is a schematic view illustrating an ocular optical systemaccording to a first embodiment of the invention.

FIG. 8A to FIG. 8D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the firstembodiment of the invention.

FIG. 9 shows detailed optical data pertaining to the ocular opticalsystem according to the first embodiment of the invention.

FIG. 10 shows aspheric parameters pertaining to the ocular opticalsystem according to the first embodiment of the invention.

FIG. 11 is a schematic view illustrating an ocular optical systemaccording to a second embodiment of the invention.

FIG. 12A to FIG. 12D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the secondembodiment of the invention.

FIG. 13 shows detailed optical data pertaining to the ocular opticalsystem according to the second embodiment of the invention.

FIG. 14 shows aspheric parameters pertaining to the ocular opticalsystem according to the second embodiment of the invention.

FIG. 15 is a schematic view illustrating an ocular optical systemaccording to a third embodiment of the invention.

FIG. 16A to FIG. 16D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the thirdembodiment of the invention.

FIG. 17 shows detailed optical data pertaining to the ocular opticalsystem according to the third embodiment of the invention.

FIG. 18 shows aspheric parameters pertaining to the ocular opticalsystem according to the third embodiment of the invention.

FIG. 19 is a schematic view illustrating an ocular optical systemaccording to a fourth embodiment of the invention.

FIG. 20A to FIG. 20D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the fourthembodiment of the invention.

FIG. 21 shows detailed optical data pertaining to the ocular opticalsystem according to the fourth embodiment of the invention.

FIG. 22 shows aspheric parameters pertaining to the ocular opticalsystem according to the fourth embodiment of the invention.

FIG. 23 is a schematic view illustrating an ocular optical systemaccording to a fifth embodiment of the invention.

FIG. 24A to FIG. 24D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the fifthembodiment of the invention.

FIG. 25 shows detailed optical data pertaining to the ocular opticalsystem according to the fifth embodiment of the invention.

FIG. 26 shows aspheric parameters pertaining to the ocular opticalsystem according to the fifth embodiment of the invention.

FIG. 27 is a schematic view illustrating an ocular optical systemaccording to a sixth embodiment of the invention.

FIG. 28A to FIG. 28D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the sixthembodiment of the invention.

FIG. 29 shows detailed optical data pertaining to the ocular opticalsystem according to the sixth embodiment of the invention.

FIG. 30 shows aspheric parameters pertaining to the ocular opticalsystem according to the sixth embodiment of the invention.

FIG. 31 is a schematic view illustrating an ocular optical systemaccording to a seventh embodiment of the invention.

FIG. 32A to FIG. 32D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the seventhembodiment of the invention.

FIG. 33 shows detailed optical data pertaining to the ocular opticalsystem according to the seventh embodiment of the invention.

FIG. 34 shows aspheric parameters pertaining to the ocular opticalsystem according to the seventh embodiment of the invention.

FIG. 35 is a schematic view illustrating an ocular optical systemaccording to an eighth embodiment of the invention.

FIG. 36A to FIG. 36D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the eighthembodiment of the invention.

FIG. 37 shows detailed optical data pertaining to the ocular opticalsystem according to the eighth embodiment of the invention.

FIG. 38 shows aspheric parameters pertaining to the ocular opticalsystem according to the eighth embodiment of the invention.

FIG. 39 is a schematic view illustrating an ocular optical systemaccording to a ninth embodiment of the invention.

FIG. 40A to FIG. 40D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the ninthembodiment of the invention.

FIG. 41 shows detailed optical data pertaining to the ocular opticalsystem according to the ninth embodiment of the invention.

FIG. 42 shows aspheric parameters pertaining to the ocular opticalsystem according to the ninth embodiment of the invention.

FIG. 43 is a schematic view illustrating an ocular optical systemaccording to a tenth embodiment of the invention.

FIG. 44A to FIG. 44D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the tenthembodiment of the invention.

FIG. 45 shows detailed optical data pertaining to the ocular opticalsystem according to the tenth embodiment of the invention.

FIG. 46 shows aspheric parameters pertaining to the ocular opticalsystem according to the tenth embodiment of the invention.

FIG. 47 is a schematic view illustrating an ocular optical systemaccording to an eleventh embodiment of the invention.

FIG. 48A to FIG. 48D illustrate a longitudinal spherical aberration andother aberrations of the ocular optical system according to the eleventhembodiment of the invention.

FIG. 49 shows detailed optical data pertaining to the ocular opticalsystem according to the eleventh embodiment of the invention.

FIG. 50 shows aspheric parameters pertaining to the ocular opticalsystem according to the eleventh embodiment of the invention.

FIG. 51 and FIG. 52 show important parameters and relation valuesthereof pertaining to the ocular optical system according to the firstthrough the ninth embodiments of the invention.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the present preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings. Wherever possible, the same reference numbers areused in the drawings and the description to refer to the same or likeparts.

In general, a ray direction of an ocular optical system V100 refers tothe following: imaging rays VI are emitted by a display screen V50,enter an eye V60 via the ocular optical system V100, and are thenfocused on a retina of the eye V60 for imaging and generating anenlarged virtual image VV at a least distance of distinct vision VD, asdepicted in FIG. 1. The following criteria for determining opticalspecifications of the present application are based on assumption that areversely tracking of the ray direction is parallel imaging rays passingthrough the ocular optical system from an eye-side and focused on thedisplay screen for imaging.

In the present specification, the description “a lens element havingpositive refracting power (or negative refracting power)” means that theparaxial refracting power of the lens element in Gaussian optics ispositive (or negative). The description “An eye-side (or display-side)surface of a lens element” only includes a specific region of thatsurface of the lens element where imaging rays are capable of passingthrough that region, namely the clear aperture of the surface. Theaforementioned imaging rays can be classified into two types, chief rayLc and marginal ray Lm. Taking a lens element depicted in FIG. 2 as anexample, I is an optical axis and the lens element is rotationallysymmetric, where the optical axis I is the axis of symmetry. The regionA of the lens element is defined as “a portion in a vicinity of theoptical axis”, and the region C of the lens element is defined as “aportion in a vicinity of a periphery of the lens element”. Besides, thelens element may also have an extending portion E extended radially andoutwardly from the region C, namely the portion outside of the clearaperture of the lens element. The extending portion E is usually usedfor physically assembling the lens element into an optical imaging lenssystem. Under normal circumstances, the imaging rays would not passthrough the extending portion E because those imaging rays only passthrough the clear aperture. The structures and shapes of theaforementioned extending portion E are only examples for technicalexplanation, the structures and shapes of lens elements should not belimited to these examples. Note that the extending portions of the lenselement surfaces depicted in the following embodiments are partiallyomitted.

The following criteria are provided for determining the shapes and theportions of lens element surfaces set forth in the presentspecification. These criteria mainly determine the boundaries ofportions under various circumstances including the portion in a vicinityof the optical axis, the portion in a vicinity of a periphery of a lenselement surface, and other types of lens element surfaces such as thosehaving multiple portions.

1. FIG. 2 is a radial cross-sectional view of a lens element. Beforedetermining boundaries of those aforesaid portions, two referentialpoints should be defined first, central point and transition point. Thecentral point of a surface of a lens element is a point of intersectionof that surface and the optical axis. The transition point is a point ona surface of a lens element, where the tangent line of that point isperpendicular to the optical axis. Additionally, if multiple transitionpoints appear on one single surface, then these transition points aresequentially named along the radial direction of the surface withnumbers starting from the first transition point. For instance, thefirst transition point (closest one to the optical axis), the secondtransition point, and the Nth transition point (farthest one to theoptical axis within the scope of the clear aperture of the surface). Theportion of a surface of the lens element between the central point andthe first transition point is defined as the portion in a vicinity ofthe optical axis. The portion located radially outside of the Nthtransition point (but still within the scope of the clear aperture) isdefined as the portion in a vicinity of a periphery of the lens element.In some embodiments, there are other portions existing between theportion in a vicinity of the optical axis and the portion in a vicinityof a periphery of the lens element; the numbers of portions depend onthe numbers of the transition point(s). In addition, the radius of theclear aperture (or a so-called effective radius) of a surface is definedas the radial distance from the optical axis I to a point ofintersection of the marginal ray Lm and the surface of the lens element.

2. Referring to FIG. 3, determining the shape of a portion is convex orconcave depends on whether a collimated ray passing through that portionconverges or diverges. That is, while applying a collimated ray to aportion to be determined in terms of shape, the collimated ray passingthrough that portion will be bended and the ray itself or its extensionline will eventually meet the optical axis. The shape of that portioncan be determined by whether the ray or its extension line meets(intersects) the optical axis (focal point) at the eye-side ordisplay-side. For instance, if the ray itself intersects the opticalaxis at the display-side of the lens element after passing through aportion, i.e. the focal point of this ray is at the display-side (seepoint R in FIG. 3), the portion will be determined as having a convexshape. On the contrary, if the ray diverges after passing through aportion, the extension line of the ray intersects the optical axis atthe eye-side of the lens element, i.e. the focal point of the ray is atthe eye-side (see point M in FIG. 3), that portion will be determined ashaving a concave shape. Therefore, referring to FIG. 3, the portionbetween the central point and the first transition point has a convexshape, the portion located radially outside of the first transitionpoint has a concave shape, and the first transition point is the pointwhere the portion having a convex shape changes to the portion having aconcave shape, namely the border of two adjacent portions.Alternatively, there is another common way for a person with ordinaryskill in the art to tell whether a portion in a vicinity of the opticalaxis has a convex or concave shape by referring to the sign of an “R”value, which is the (paraxial) radius of curvature of a lens surface.The R value which is commonly used in conventional optical designsoftware such as Zemax and CodeV. The R value usually appears in thelens data sheet in the software. For an eye-side surface, positive Rmeans that the eye-side surface is convex, and negative R means that theeye-side surface is concave. Conversely, for a display-side surface,positive R means that the display-side surface is concave, and negativeR means that the display-side surface is convex. The result found byusing this method should be consistent as by using the other waymentioned above, which determines surface shapes by referring to whetherthe focal point of a collimated ray is at the eye-side or thedisplay-side.

3. For none transition point cases, the portion in a vicinity of theoptical axis is defined as the portion between 0˜50% of the effectiveradius (radius of the clear aperture) of the surface, whereas theportion in a vicinity of a periphery of the lens element is defined asthe portion between 50˜100% of effective radius (radius of the clearaperture) of the surface.

Referring to the first example depicted in FIG. 4, only one transitionpoint, namely a first transition point, appears within the clearaperture of the display-side surface of the lens element. Portion I is aportion in a vicinity of the optical axis, and portion II is a portionin a vicinity of a periphery of the lens element. The portion in avicinity of the optical axis is determined as having a concave surfacedue to the R value at the display-side surface of the lens element ispositive. The shape of the portion in a vicinity of a periphery of thelens element is different from that of the radially inner adjacentportion, i.e. the shape of the portion in a vicinity of a periphery ofthe lens element is different from the shape of the portion in avicinity of the optical axis; the portion in a vicinity of a peripheryof the lens element has a convex shape.

Referring to the second example depicted in FIG. 5, a first transitionpoint and a second transition point exist on the eye-side surface(within the clear aperture) of a lens element. In which portion I is theportion in a vicinity of the optical axis, and portion III is theportion in a vicinity of a periphery of the lens element. The portion ina vicinity of the optical axis has a convex shape because the R value atthe eye-side surface of the lens element is positive. The portion in avicinity of a periphery of the lens element (portion III) has a convexshape. What is more, there is another portion having a concave shapeexisting between the first and second transition point (portion II).

Referring to a third example depicted in FIG. 6, no transition pointexists on the eye-side surface of the lens element. In this case, theportion between 0˜50% of the effective radius (radius of the clearaperture) is determined as the portion in a vicinity of the opticalaxis, and the portion between 50˜100% of the effective radius isdetermined as the portion in a vicinity of a periphery of the lenselement. The portion in a vicinity of the optical axis of the eye-sidesurface of the lens element is determined as having a convex shape dueto its positive R value, and the portion in a vicinity of a periphery ofthe lens element is determined as having a convex shape as well.

FIG. 7 is a schematic view illustrating an ocular optical systemaccording to the first embodiment of the invention, and FIG. 8A to FIG.8D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the first embodiment of theinvention. Referring to FIG. 7, an ocular optical system 10 according tothe first embodiment of the invention is used for imaging of imagingrays entering an eye of an observer via the ocular optical system 10 anda pupil 2 of the eye of the observer from a display screen 100. A sidefacing towards the eye is an eye-side, a side facing towards the displayscreen 100 is a display-side. The ocular optical system 10 includes afirst lens element 3, a second lens element 4, and a third lens element5 from the eye-side to the display-side in order along an optical axis Iof the ocular optical system 10. When the rays emitted by the displayscreen 100 enter the ocular optical system 10, pass through third lenselement 5, the second lens elements 4, and the first lens element 3 inorder, and enter the eye of the observer via the pupil 2, an image isformed on a retina of the eye.

The first lens element 3, the second lens element 4, and the third lenselement 5 each include an eye-side surface 31, 41, 51 facing theeye-side and allowing the imaging rays to pass through and adisplay-side surface 32, 42, 52 facing the display-side and allowing theimaging rays to pass through. In order to meet the demand for lighterproducts, the first lens element 3, the second lens element 4, and thethird lens element 5 all have refracting power. Besides, the first lenselement 3, the second lens element 4, and the third lens element 5 aremade of plastic material; nevertheless, the material of the first lenselement 3, the second lens element 4, and the third lens element 5 isnot limited thereto.

The first lens element 3 has positive refracting power. The eye-sidesurface 31 of the first lens element 3 is a convex surface, and has aconvex portion 311 in a vicinity of the optical axis I and a convexportion 313 in a vicinity of a periphery of the first lens element 3.The display-side surface 32 of the first lens element 3 is a convexsurface, and has a convex portion 321 in a vicinity of the optical axisI and a convex portion 323 in a vicinity of a periphery of the firstlens element 3.

The second lens element 4 has positive refracting power. The eye-sidesurface 41 of the second lens element 4 is a convex surface, and has aconvex portion 411 in a vicinity of the optical axis I and a convexportion 413 in a vicinity of a periphery of the second lens element 4.The display-side surface 42 of the second lens element 4 is a convexsurface, and has a convex portion 421 in a vicinity of the optical axisI and a convex portion 423 in a vicinity of a periphery of the secondlens element 4.

The third lens element 5 has negative refracting power. The eye-sidesurface 51 of the third lens element 5 is a concave surface, and has aconcave portion 512 in a vicinity of the optical axis I and a concaveportion 514 in a vicinity of a periphery of the third lens element 5.The display-side surface 52 of the third lens element 5 has a concaveportion 522 in a vicinity of the optical axis I and a convex portion 523in a vicinity of a periphery of the third lens element 5.

Further, in the present embodiment, only the aforesaid lens elementshave refracting power, and the ocular optical system 10 includes onlythe three lens elements having the refracting power.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the first embodiment is indicated inFIG. 1 and FIG. 51. wherein

EPD represents an exit pupil diameter of the ocular optical system 10corresponding to a diameter of the pupil 2 of the observer, which isapproximately 3 mm during the day and approximately 7 mm at night, asdepicted in FIG. 1;

ER (eye relief) represents an exit pupil distance, which is a distancefrom the pupil 2 of the observer to the first lens element 3 along theoptical axis I;

ω represents a half apparent field of view, which is one half the fieldof view of the observer, as depicted in FIG. 1;

T1 represents a thickness of the first lens element 3 along the opticalaxis I;

T2 represents a thickness of the second lens element 4 along the opticalaxis I;

T3 represents a thickness of the third lens element 5 along the opticalaxis I;

G12 represents a distance from the display-side surface 32 of the firstlens element 3 to the eye-side surface 41 of the second lens element 4along the optical axis I, which is an air gap from the first lenselement 3 to the second lens element 4 along the optical axis I;

G23 represents a distance from the display-side surface 42 of the secondlens element 4 to the eye-side surface 51 of the third lens element 5along the optical axis I, which is an air gap from the second lenselement 4 to the third lens element 5 along the optical axis I;

G3D represents a distance from the display-side surface 52 of the thirdlens element 5 to the display screen 100 along the optical axis I, whichis an air gap from the third lens element 5 to the display screen 100along the optical axis I;

DLD represents a diagonal length of the display screen 100 correspondingto one single pupil 2 of the observer, as depicted in FIG. 1;

a least distance of distinct vision is the closest distance that the eyeis able to clearly focus on, which is normally 250 millimeters (mm) foryoung people, i.e., the least distance of distinct vision VD depicted inFIG. 1;

ALT represents a sum of the thicknesses of the first lens element 3, thesecond lens element 4, and the third lens element 5 along the opticalaxis I, i.e., a sum of T1, T2, and T3;

AGG represents a sum of two air gaps from the first lens element to thethird lens element along the optical axis, i.e., a sum of G12 and G23;

TTL represents a distance from the eye-side surface 31 of the first lenselement 3 to the display screen 100 along the optical axis I;

TL represents a distance from the eye-side surface 31 of the first lenselement 3 to the display-side surface 52 of the third lens element 5along the optical axis I;

SL represents a system length, which is a distance from the pupil 2 ofthe observer to the display screen 100 along the optical axis I; and

EFL represents an effective focal length of the ocular optical system10.

Besides, it is further defined that:

f1 is a focal length of the first lens element 3;

f2 is a focal length of the second lens element 4;

f3 is a focal length of the third lens element 5;

n1 is a refractive index of the first lens element 3;

n2 is a refractive index of the second lens element 4;

n3 is a refractive index of the third lens element 5;

ν1 is an Abbe number of the first lens element 3, and the Abbe number isalso known as a dispersion coefficient;

ν2 is an Abbe number of the second lens element 4;

ν3 is an Abbe number of the third lens element 5;

D1 is a diameter of a clear aperture of the eye-side surface 31 of thefirst lens element 3;

D2 is a diameter of a clear aperture of the eye-side surface 41 of thesecond lens element 4; and

D3 is a diameter of a clear aperture of the eye-side surface 51 of thethird lens element 5.

Other detailed optical data in the first embodiment are indicated inFIG. 9. In the first embodiment, the effective focal length (EFL) (i.e.system focal length) of the ocular optical system 10 is 47.427 mm, thehalf apparent field of view (ω) thereof is 42.775°, TTL thereof is66.543 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 35.000 mm,and SL thereof is 77.236 mm. Among them, the effective radius in FIG. 9refers to one half the diameter of the clear aperture.

Further, in the present embodiment, the eye-side surface 31 and thedisplay-side surface 32 of the first lens element 3, the eye-sidesurface 41 and the display-side surface 42 of the second lens element 4,and the eye-side surface 51 and the display-side surface 52 of the thirdlens element 5 (six surfaces in total) are the aspheric surfaces. Theaspheric surfaces are defined by the following formula.

$\begin{matrix}{{Z(Y)} = {{\frac{Y^{2}}{R}/\left( {1 + \sqrt{1 - {\left( {1 + K} \right)\frac{Y^{2}}{R^{2}}}}} \right)} + {\sum\limits_{i = 1}^{n}{a_{i} \times Y^{i}}}}} & (1)\end{matrix}$

wherein

Y: a distance from a point on an aspheric curve to the optical axis I;

Z: a depth of the aspheric surface (a vertical distance between thepoint on the aspheric surface that is spaced from the optical axis I bythe distance Y and a tangent plane tangent to a vertex of the asphericsurface on the optical axis I);

R: a radius of curvature of the surface of the lens element close to theoptical axis I;

K: a conic constant;

a_(i): the i^(th) aspheric coefficient.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 10. In FIG. 10, the referential number 31 is one rowthat represents the aspheric coefficient of the eye-side surface 31 ofthe first lens element 3, and the reference numbers in other rows can bededuced from the above.

Referring to FIG. 8A to FIG. 8D, FIG. 8A to FIG. 8D illustrate theaberrations of the ocular optical system 10 of the first embodiment,which are the aberrations obtained based on the assumption that thereversely tracking of the ray direction is the parallel imaging rayspassing through the pupil 2 and the ocular optical system 10 in orderfrom the eye-side and focused on the display screen 100 for imaging. Inthe present embodiment, each aberration behavior shown in each of theaberrations can decide the corresponding aberration behavior for imagingof the imaging rays from the display screen 100 on the retina of the eyeof the observer. In other words, when each aberration behavior in eachof the aberrations is smaller, each aberration behavior for imaging onthe retina of the eye of the observer may also be smaller so the imagewith better imaging quality can be observed by the observer. FIG. 8Aillustrates the longitudinal spherical aberration when a pupil radiusthereof is 2 mm in the first embodiment. FIG. 8B and FIG. 8C illustratea field curvature aberration in a sagittal direction and a fieldcurvature aberration in a tangential direction on the display screen 100when wavelengths are 486 nm, 587 nm and 656 nm in the first embodiment.FIG. 8D illustrates a distortion aberration on the display screen 100when wavelengths are 486 nm, 587 nm and 656 nm in the first embodiment.In FIG. 8A which illustrates the longitudinal spherical aberration inthe first embodiment, the curve of each wavelength is close to oneanother and approaches the center position, which indicates that theoff-axis ray of each wavelength at different heights is concentratedaround the imaging point. The skew margin of the curve of eachwavelength indicates that the imaging point deviation of the off-axisray at different heights is controlled within a range of ±0.48 mm.Hence, it is evident that the spherical aberration of the samewavelength can be significantly improved according to the presentembodiment. In addition, the curves of the three representativewavelengths (red, green, and blue) are close to one another, whichindicates that the imaging positions of the rays with differentwavelengths are rather concentrated; therefore, the chromatic aberrationcan be significantly improved as well.

In FIG. 8B and FIG. 8C which illustrate two diagrams of field curvatureaberrations, the focal length variation of the three representativewavelengths within the entire field of view falls within the range of±0.8 mm, which indicates that aberration of the optical system providedin the first embodiment can be effectively eliminated. In FIG. 8D, thediagram of distortion aberration shows that the distortion aberration inthe first embodiment can be maintained within the range of ±21%, whichindicates that the distortion aberration in the first embodiment cancomply with the imaging quality requirement of the optical system.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the first embodiment can have the favorableimaging quality, given that SL is shortened to about 77.236 mm. As aresult, according to the first embodiment, the length of the opticalsystem can be shortened and the apparent field of view can be enlargedwithout sacrificing the favorable optical properties. In this way, theproduct design with miniaturization, low aberration and large apparentfield of view taken into account can be realized.

FIG. 11 is a schematic view illustrating an ocular optical systemaccording to the second embodiment of the invention, and FIG. 12A toFIG. 12D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the secondembodiment of the invention. With reference to FIG. 11, the ocularoptical system 10 according to the second embodiment of the invention issimilar to that provided in the first embodiment, while the differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. Further, in thepresent embodiment, the eye-side surface 41 of the second lens element 4has a convex portion 411 in a vicinity of the optical axis I and aconcave portion 414 in a vicinity of a periphery of the second lenselement 4. Moreover, in the present embodiment, the eye-side surface 51of the third lens element 5 has a convex portion 511 in a vicinity ofthe optical axis I and a concave portion 514 in a vicinity of aperiphery of the third lens element 5. For clear illustration, it shouldbe mentioned that the same reference numbers of the concave portions andthe convex portions in the two embodiments are omitted from FIG. 11.

Detailed optical data of the ocular optical system 10 in the secondembodiment are indicated in FIG. 13. In the second embodiment, EFL ofthe ocular optical system 10 is 48.928 mm, ω thereof is 41.000°, TTLthereof is 61.725 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is35.000 mm, and SL thereof is 79.881 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 14 according to the second embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the second embodiment is indicated inFIG. 51.

In FIG. 12A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the second embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±1.1 mm. In FIG. 12B and FIG. 12C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.8 mm. In FIG. 12D, thediagram of distortion aberration shows that the distortion aberration inthe second embodiment can be maintained within the range of ±20%.Accordingly, compared to the existing ocular optical system, the secondembodiment can have the favorable imaging quality, given that SL isshortened to about 79.881 mm.

According to the above description, compared to the first embodiment,the advantages of the second embodiment are as follows. The distortionin the second embodiment is less than that in the first embodiment.Besides, because a thickness difference between portions in a vicinityof the optical axis and in a vicinity of a periphery of the lens elementin the second embodiment is less than that of the first embodiment, theocular optical system in the second embodiment is, in comparison withthat provided in the first embodiment, easier to be manufactured andthus has higher yield.

FIG. 15 is a schematic view illustrating an ocular optical systemaccording to the third embodiment of the invention, and FIG. 16A to FIG.16D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the third embodiment of theinvention. With reference to FIG. 15, the ocular optical system 10according to the third embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3, 4, and 5 in these two embodiments aredifferent to some extent. Further, in the present embodiment, theeye-side surface 31 of the first lens element 3 has a convex portion 311in a vicinity of the optical axis I and a concave portion 314 in avicinity of a periphery of the first lens element 3. For clearillustration, it should be mentioned that the same reference numbers ofthe concave portions and the convex portions in the two embodiments areomitted from FIG. 15.

Detailed optical data of the ocular optical system 10 in the thirdembodiment are indicated in FIG. 17. In the third embodiment, EFL of theocular optical system 10 is 33.624 mm, ω thereof is 56.157°, TTL thereofis 50.411 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 35.000mm, and SL thereof is 58.411 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 18 according to the third embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the third embodiment is indicated inFIG. 51.

In FIG. 16A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the third embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.52 mm. In FIG. 16B and FIG. 16C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±3.6 mm. In FIG. 16D, thediagram of distortion aberration shows that the distortion aberration inthe third embodiment can be maintained within the range of ±30%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the third embodiment can have the favorableimaging quality, given that the system length SL is shortened to about58.411 mm.

According to the above description, compared to the first embodiment,the advantages of the third embodiment are as follows. The system lengthSL of the ocular optical system 10 in the third embodiment is less thanthe system length SL in the first embodiment; the half apparent field ofview ω in the third embodiment is greater than the half apparent fieldof view ω in the first embodiment.

FIG. 19 is a schematic view illustrating an ocular optical systemaccording to the fourth embodiment of the invention, and FIG. 20A toFIG. 20D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the fourthembodiment of the invention. With reference to FIG. 19, the ocularoptical system 10 according to the fourth embodiment of the invention issimilar to that provided in the first embodiment, while differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. Further, in thepresent embodiment, the eye-side surface 41 of the second lens element 4has a convex portion 411 in a vicinity of the optical axis I and aconcave portion 414 in a vicinity of a periphery of the second lenselement 4. For clear illustration, it should be mentioned that the samereference numbers of the concave portions and the convex portions in thetwo embodiments are omitted from FIG. 19.

Detailed optical data of the ocular optical system 10 in the fourthembodiment are indicated in FIG. 21. In the fourth embodiment, EFL ofthe ocular optical system 10 is 61.299 mm, ω thereof is 40.975°, TTLthereof is 86.102 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is39.459 mm, and SL thereof is 96.558 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 22 according to the fourth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the fourth embodiment is indicated inFIG. 51.

In FIG. 20A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the fourth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.54 mm. In FIG. 20B and FIG. 20C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.9 mm. In FIG. 20D, thediagram of distortion aberration shows that the distortion aberration inthe fourth embodiment can be maintained within the range of ±28%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the fourth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about96.558 mm.

According to the above description, compared to the first embodiment,the advantages of the fourth embodiment are as follows. Because athickness difference between portions in a vicinity of the optical axisand in a vicinity of a periphery of the lens element in the fourthembodiment is less than that of the first embodiment, the ocular opticalsystem in the fourth embodiment is, in comparison with that provided inthe first embodiment, easier to be manufactured and thus has higheryield.

FIG. 23 is a schematic view illustrating an ocular optical systemaccording to the fifth embodiment of the invention, and FIG. 24A to FIG.24D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the fifth embodiment of theinvention. With reference to FIG. 23, the ocular optical system 10according to the fifth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences are as follows.The optical data, the aspheric coefficients, and the parameters of thelens elements 3, 4, and 5 in these two embodiments are different to someextent. Further, in the present embodiment, the eye-side surface 31 ofthe first lens element 3 has a convex portion 311 in a vicinity of theoptical axis I and a concave portion 314 in a vicinity of a periphery ofthe first lens element 3. For clear illustration, it should be mentionedthat the same reference numbers of the concave portions and the convexportions in the two embodiments are omitted from FIG. 23.

Detailed optical data of the ocular optical system 10 in the fifthembodiment are indicated in FIG. 25. In the fifth embodiment, EFL of theocular optical system 10 is 43.758 mm, ω thereof is 40.996°, TTL thereofis 62.359 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 36.608mm, and SL thereof is 71.570 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 26 according to the fifth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the fifth embodiment is indicated inFIG. 51.

In FIG. 24A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the fifth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.73 mm. In FIG. 24B and FIG. 24C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±2.9 mm. In FIG. 24D, thediagram of distortion aberration shows that the distortion aberration inthe fifth embodiment can be maintained within the range of ±6%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the fifth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about71.570 mm.

According to the above description, compared to the first embodiment,the advantages of the fifth embodiment are as follows. The system lengthSL of the fifth embodiment is less than that of the first embodiment.The distortion of the fifth embodiment is less than the distortion ofthe first embodiment.

FIG. 27 is a schematic view illustrating an ocular optical systemaccording to the sixth embodiment of the invention, and FIG. 28A to FIG.28D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the sixth embodiment of theinvention. With reference to FIG. 27, the ocular optical system 10according to the sixth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3, 4, and 5 in these two embodiments aredifferent to some extent. For clear illustration, it should be mentionedthat the same reference numbers of the concave portions and the convexportions in the two embodiments are omitted from FIG. 27.

Detailed optical data of the ocular optical system 10 in the sixthembodiment are indicated in FIG. 29. In the sixth embodiment, EFL of theocular optical system 10 is 45.853 mm, ω thereof is 40.551°, TTL thereofis 57.724 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 31.956mm, and SL thereof is 79.996 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 30 according to the sixth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the sixth embodiment is indicated inFIG. 52.

In FIG. 28A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the sixth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.45 mm. In FIG. 28B and FIG. 28C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±4 mm. In FIG. 28D, the diagramof distortion aberration shows that the distortion aberration in thesixth embodiment can be maintained within the range of ±19%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the sixth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about79.996 mm.

According to the above description, compared to the first embodiment,the advantages of the sixth embodiment are as follows. The longitudinalspherical aberration in the sixth embodiment is less than thelongitudinal spherical aberration in the first embodiment; and thedistortion in the sixth embodiment is less than the distortion in thefirst embodiment.

FIG. 31 is a schematic view illustrating an ocular optical systemaccording to the seventh embodiment of the invention, and FIG. 32A toFIG. 32D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the seventhembodiment of the invention. With reference to FIG. 31, the ocularoptical system 10 according to the seventh embodiment of the inventionis similar to that provided in the first embodiment, while thedifferences therebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. For clearillustration, it should be mentioned that the same reference numbers ofthe concave portions and the convex portions in the two embodiments areomitted from FIG. 31.

Detailed optical data of the ocular optical system 10 in the seventhembodiment are indicated in FIG. 33. In the seventh embodiment, EFL ofthe ocular optical system 10 is 61.919 mm, ω thereof is 41.000°, TTLthereof is 80.258 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is44.369 mm, and SL thereof is 92.925 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 34 according to the seventh embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the seventh embodiment is indicatedin FIG. 52.

In FIG. 32A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the seventh embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.9 mm. In FIG. 32B and FIG. 32C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.9 mm. In FIG. 32D, thediagram of distortion aberration shows that the distortion aberration inthe seventh embodiment can be maintained within the range of ±19%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the seventh embodiment can have the favorableimaging quality, given that the system length SL is shortened to about92.925 mm.

According to the above description, compared to the first embodiment,the advantages of the seventh embodiment are as follows. The distortionaberration of the seventh embodiment is less than the distortionaberration of the first embodiment. Besides, because a thicknessdifference between portions in a vicinity of the optical axis and in avicinity of a periphery of the lens element in the seventh embodiment isless than that of the first embodiment, the ocular optical system in theseventh embodiment is, in comparison with that provided in the firstembodiment, easier to be manufactured and thus has higher yield.

FIG. 35 is a schematic view illustrating an ocular optical systemaccording to the eighth embodiment of the invention, and FIG. 36A toFIG. 36D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the eighthembodiment of the invention. With reference to FIG. 35, the ocularoptical system 10 according to the eighth embodiment of the invention issimilar to that provided in the first embodiment, while the differencestherebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. For clearillustration, it should be mentioned that the same reference numbers ofthe concave portions and the convex portions in the two embodiments areomitted from FIG. 35.

Detailed optical data of the ocular optical system 10 in the eighthembodiment are indicated in FIG. 37. In the eighth embodiment, EFL ofthe ocular optical system 10 is 45.381 mm, ω thereof is 40.977°, TTLthereof is 75.038 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is35.240 mm, and SL thereof is 85.651 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 38 according to the eighth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the eighth embodiment is indicated inFIG. 52.

In FIG. 36A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the eighth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±1.1 mm. In FIG. 36B and FIG. 36C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±3.5 mm. In FIG. 36D, thediagram of distortion aberration shows that the distortion aberration inthe eighth embodiment can be maintained within the range of ±13%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the eighth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about85.651 mm.

According to the above description, compared to the first embodiment,the advantages of the eighth embodiment are as follows. The distortionaberration of the eighth embodiment is less than the distortionaberration of the first embodiment. Besides, because a thicknessdifference between portions in a vicinity of the optical axis and in avicinity of a periphery of the lens element in the eighth embodiment isless than that of the first embodiment, the ocular optical system in theeighth embodiment is, in comparison with that provided in the firstembodiment, easier to be manufactured and thus has higher yield.

FIG. 39 is a schematic view illustrating an ocular optical systemaccording to the ninth embodiment of the invention, and FIG. 40A to FIG.40D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the ninth embodiment of theinvention. With reference to FIG. 39, the ocular optical system 10according to the ninth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3, 4, and 5 in these two embodiments aredifferent to some extent. Moreover, in this embodiment, the eye-sidesurface 41 of the second lens element 4 has a convex portion 411 in avicinity of the optical axis I and a concave portion 414 in a vicinityof a periphery of the second lens element 4. For clear illustration, itshould be mentioned that the same reference numbers of the concaveportions and the convex portions in the two embodiments are omitted fromFIG. 39.

Detailed optical data of the ocular optical system 10 in the ninthembodiment are indicated in FIG. 41. In the ninth embodiment, EFL of theocular optical system 10 is 50.614 mm, ω thereof is 41.000°, TTL thereofis 67.726 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 35.000mm, and SL thereof is 79.994 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 42 according to the ninth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the ninth embodiment is indicated inFIG. 52.

In FIG. 40A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the ninth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.4 mm. In FIG. 40B and FIG. 40C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.5 mm. In FIG. 40D, thediagram of distortion aberration shows that the distortion aberration inthe ninth embodiment can be maintained within the range of ±21%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the ninth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about79.994 mm.

According to the above description, compared to the first embodiment,the advantages of the ninth embodiment are as follows. The longitudinalspherical aberration of the ninth embodiment is less than that of thefirst embodiment. Besides, because a thickness difference betweenportions in a vicinity of the optical axis and in a vicinity of aperiphery of the lens element in the ninth embodiment is less than thatof the first embodiment, the ocular optical system in the ninthembodiment is, in comparison with that provided in the first embodiment,easier to be manufactured and thus has higher yield.

FIG. 43 is a schematic view illustrating an ocular optical systemaccording to the tenth embodiment of the invention, and FIG. 44A to FIG.44D illustrate a longitudinal spherical aberration and other aberrationsof the ocular optical system according to the tenth embodiment of theinvention. With reference to FIG. 43, the ocular optical system 10according to the tenth embodiment of the invention is similar to thatprovided in the first embodiment, while the differences therebetween areas follows. The optical data, the aspheric coefficients, and theparameters of the lens elements 3, 4, and 5 in these two embodiments aredifferent to some extent. Moreover, in this embodiment, the eye-sidesurface 41 of the second lens element 4 has a convex portion 411 in avicinity of the optical axis I and a concave portion 414 in a vicinityof a periphery of the second lens element 4. For clear illustration, itshould be mentioned that the same reference numbers of the concaveportions and the convex portions in the two embodiments are omitted fromFIG. 43.

Detailed optical data of the ocular optical system 10 in the tenthembodiment are indicated in FIG. 45. In the tenth embodiment, EFL of theocular optical system 10 is 47.427 mm, ω thereof is 42.775°, TTL thereofis 66.543 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is 35.000mm, and SL thereof is 77.236 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 46 according to the tenth embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the tenth embodiment is indicated inFIG. 52.

In FIG. 44A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the tenth embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.6 mm. In FIG. 44B and FIG. 44C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±0.6 mm. In FIG. 44D, thediagram of distortion aberration shows that the distortion aberration inthe tenth embodiment can be maintained within the range of ±16%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the tenth embodiment can have the favorableimaging quality, given that the system length SL is shortened to about77.236 mm.

According to the above description, compared to the first embodiment,the advantages of the tenth embodiment are as follows. The fieldcurvature of the tenth embodiment is less than that of the firstembodiment. The distortion of the tenth embodiment is less than that ofthe first embodiment. Besides, because a thickness difference betweenportions in a vicinity of the optical axis and in a vicinity of aperiphery of the lens element in the tenth embodiment is less than thatof the first embodiment, the ocular optical system in the tenthembodiment is, in comparison with that provided in the first embodiment,easier to be manufactured and thus has higher yield.

FIG. 47 is a schematic view illustrating an ocular optical systemaccording to the eleventh embodiment of the invention, and FIG. 48A toFIG. 48D illustrate a longitudinal spherical aberration and otheraberrations of the ocular optical system according to the eleventhembodiment of the invention. With reference to FIG. 47, the ocularoptical system 10 according to the eleventh embodiment of the inventionis similar to that provided in the first embodiment, while thedifferences therebetween are as follows. The optical data, the asphericcoefficients, and the parameters of the lens elements 3, 4, and 5 inthese two embodiments are different to some extent. Moreover, in thisembodiment, the eye-side surface 41 of the second lens element 4 has aconvex portion 411 in a vicinity of the optical axis I and a concaveportion 414 in a vicinity of a periphery of the second lens element 4.For clear illustration, it should be mentioned that the same referencenumbers of the concave portions and the convex portions in the twoembodiments are omitted from FIG. 47.

Detailed optical data of the ocular optical system 10 in the eleventhembodiment are indicated in FIG. 49. In the eleventh embodiment, EFL ofthe ocular optical system 10 is 49.186 mm, ω thereof is 41.000°, TTLthereof is 61.444 mm, EPD thereof is 2.000 mm, 0.5 times DLD thereof is35.000 mm, and SL thereof is 80.000 mm.

The aspheric coefficients of the eye-side surfaces 31, 41, and 51 andthe display-side surfaces 32, 42, and 52 in the formula (1) areindicated in FIG. 50 according to the eleventh embodiment.

In addition, the relationship among the important parameters pertainingto the ocular optical system 10 in the eleventh embodiment is indicatedin FIG. 52.

In FIG. 48A which illustrates the longitudinal spherical aberration whenthe pupil radius is 2.0000 mm according to the eleventh embodiment, theimaging point deviation of the off-axis ray at different heights iscontrolled within a range of ±0.5 mm. In FIG. 48B and FIG. 48C whichillustrate two diagrams of field curvature aberrations, the focal lengthvariation of the three representative wavelengths within the entirefield of view falls within the range of ±1.9 mm. In FIG. 48D, thediagram of distortion aberration shows that the distortion aberration inthe eleventh embodiment can be maintained within the range of ±18%.Accordingly, compared to the existing ocular optical system, the ocularoptical system provided in the eleventh embodiment can have thefavorable imaging quality, given that the system length SL is shortenedto about 80.000 mm.

According to the above description, compared to the first embodiment,the advantage of the eleventh embodiment is as follows. The distortionof the eleventh embodiment is less than that of the first embodiment.

FIG. 51 and FIG. 52 are table diagrams showing the optical parametersprovided in the foregoing eleven embodiments. If the relationship amongthe optical parameters in the ocular optical system 10 provided in theembodiments of the invention satisfies at least one of the followingconditions, the design of the ocular optical system with favorableoptical performance and the reduced length in whole becomes technicalfeasible:

1. If the system can satisfy the following condition, the aberrations ofthe first lens element 3 and the second lens element 4 can be corrected:T3/G23≤4.3. Preferably, 0.1≤T3/G23≤4.3 is satisfied. If the followingcondition can be satisfied, the aberrations of the first lens element 3,the second lens element 4, and the third lens element 5 may be slightlyadjusted: G3D/T3≤3.51. Preferably, 0.16≤G3D/T3≤3.51 is satisfied.

2. Because 250 mm is the least distance of distinct vision of youngpeople (the closest distance that the eye of young people is able toclearly focus on), the magnifying power of the system can approach aratio of 250 mm and EFL. Therefore, if the following condition can besatisfied, the magnifying power of the system is unlikely to be so largethat can increase the thickness and manufacturing difficulty of the lenselement: 250 mm/EFL≤25. If the following condition can be furthersatisfied, EFL is unlikely to be so long that can affect the systemlength: 2.5≤250 mm/EFL≤25.

3. If the following condition can be satisfied, the observer is unlikelyto experience the narrow vision: 40°≤ω. If the following condition canbe further satisfied, a designing difficulty is not increased: 40° ω60°.

4. If the system can satisfy at least one of the following conditions:0.1≤G23/G3D≤10, 0.7≤AAG/T2≤25, 0.5≤T1/T2≤10, 2.2≤ALT/T2≤50,0.7≤T1/T3≤10, and 0.4≤AAG/G3D≤20, the thickness and interval of eachlens element can be maintained at an appropriate value, so as to preventthe slimness of the ocular optical system 10 in whole from beingaffected by any overly large parameter, or prevent the assembly frombeing affected or the manufacturing difficulty from increased by the anyoverly small parameter.

5. If the system can satisfy at least one of the following conditions:EFL/ALT≤1.8, EFL/AAG≤6.2, and 1.23≤TTL/EFL≤10 (more preferably, at leastone of the following conditions is to be satisfied: 0.17≤EFL/ALT≤1.8 and0.3≤EFL/AAG≤6.2), the EFL and various optical parameters can bemaintained at an appropriate value, so as to prevent the aberrationcorrection of the ocular optical system 10 in whole from being affectedby any overly large parameter, or prevent the assembly from beingaffected or the manufacturing difficulty from increased by the anyoverly small parameter.

6. If the system can satisfy at least one of the following conditions:ER/T1≤8, 1≤ALT/ER≤10, ER/T3≤4.31, 3≤SL/ER≤29, (ER+G12+G3D)/T3≤8.01,ER/G23≤20, (ER+G12+G3D)/G23≤36 (more preferably, at least one of thefollowing conditions is to be satisfied: 0.4≤ER/T1≤8, 0.2≤ER/T3≤4.31,0.5≤(ER+G12+G3D)/T3≤8.01, 0.45≤ER/G23≤20, 0.3≤(ER+G12+G3D)/G23≤36), theexit pupil distance and the optical parameters of the lens elements canbe maintained at an appropriate value, so as to prevent any parameterfrom being so large that can cause the distance between the eye and theocular optical system 10 to be so large or small that can make the eyeuncomfortable, or prevent the assembly from being affected or themanufacturing difficulty from increased by the any overly smallparameter.

However, due to the unpredictability of the design of an optical system,with the framework set forth in the embodiments of the invention, theocular optical system satisfying said conditions can be characterized bythe reduced system length, the enlarged available aperture, theincreased apparent field of view, the improved imaging quality, or theimproved assembly yield, such that the shortcomings described in therelated art can be better prevented.

To sum up, the ocular optical system 10 described in the embodiments ofthe invention may have at least one of the following advantages and/orachieve at least one of the following effects.

1. The longitudinal spherical aberrations; field curvature aberrations,and distortion aberrations provided in the embodiments of the inventionall comply with usage specifications. Moreover, the off-axis rays withdifferent heights and the three representative wavelengths (486 nm, 587nm, and 656 nm) are all gathered around imaging points, and according toa deviation range of each curve, it can be observed that deviations ofthe imaging points of the off-axis rays with different heights are allcontrolled and thus capable of suppressing spherical aberrations, imageaberrations, and distortion. With reference to the imaging quality data,distances among the three representative wavelengths (486 nm, 587 nm,and 656 nm) are fairly close, which indicates that rays with differentwavelengths in the embodiments of the invention can be well concentratedunder different circumstances to provide the capability of suppressingdispersion. As such, it can be known from the above that, theembodiments of the invention can provide favorable optical properties.

2. The display-side surface 42 of the second lens element 4 has a convexportion 421 in a vicinity of the optical axis I and a convex portion 423in a vicinity of a periphery of the second lens element 4, the eye-sidesurface 41 of the second lens element 4 has a convex portion 411 in avicinity of the optical axis I, and the eye-side surface 51 of the thirdlens element 5 has a concave portion 514 in a vicinity of a periphery ofthe third lens element 5, which are conducive to magnify the image.

3. In addition, system limitations may be further added by using anycombination relation of the parameters selected from the providedembodiments to implement the system design with the same framework setforth in the embodiments of the invention. In view of theunpredictability of the design of an optical system, with the frameworkset forth in the embodiments of the invention, the ocular optical systemsatisfying said conditions can be characterized by the reduced systemlength, the enlarged exit pupil diameter, the improved imaging quality,or the improved assembly yield, such that the shortcomings described inthe related art can be better prevented.

4. The aforementioned limitation relations are provided in an exemplarysense and can be randomly and selectively combined and applied to theembodiments of the invention in different manners; the invention shouldnot be limited to the above examples. In implementation of theinvention, apart from the above-described relations, it is also possibleto add additional detailed structure such as more concave and convexcurvatures arrangement of a specific lens element or a plurality of lenselements so as to enhance control of system property and/or resolution.For example, it is optional to form an additional convex portion in thevicinity of the optical axis on the eye-side surface of the first lenselement. It should be noted that the above-described details can beoptionally combined and applied to the other embodiments of theinvention under the condition where they are not in conflict with oneanother.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the structure of the presentinvention without departing from the scope or spirit of the invention.In view of the foregoing, it is intended that the present inventioncover modifications and variations of this invention provided they fallwithin the scope of the following claims and their equivalents.

What is claimed is:
 1. An ocular optical system, for imaging of imagingrays entering an eye of an observer via the ocular optical system from adisplay screen, a side facing towards the eye being an eye-side, a sidefacing towards the display screen being a display-side, the ocularoptical system comprising a first lens element, a second lens element,and a third lens element from the eye-side to the display-side in orderalong an optical axis, the first lens element, the second lens element,and the third lens element each comprising an eye-side surface and adisplay-side surface; the first lens element having refracting power;the display-side surface of the second lens element having a convexportion in a vicinity of the optical axis; and the display-side surfaceof the third lens element having a concave portion in a vicinity of theoptical axis, the third lens element having refracting power, whereinlens elements of the ocular optical system having refracting power areonly the first lens element, the second lens element, and the third lenselement, and the ocular optical system satisfies:T3/G23≤4.3; andG3D/T3≤3.51, where T3 is a thickness of the third lens element along theoptical axis, G23 is an air gap from the second lens element to thethird lens element along the optical axis, and G3D is a distance fromthe third lens element to the display screen along the optical axis. 2.The ocular optical system according to claim 1, wherein the ocularoptical system further satisfies: ER/T1≤8, where ER is a distance from apupil of the eye of the observer to the first lens element along theoptical axis, and T1 is a thickness of the first lens element along theoptical axis.
 3. The ocular optical system according to claim 1, whereinthe ocular optical system further satisfies: 0.1≤G23/G3D≤10.
 4. Theocular optical system according to claim 1, wherein the ocular opticalsystem further satisfies: EFL/ALT≤1.8, where EFL is an effective focallength of the ocular optical system, and ALT is a sum of thicknesses ofthe first lens element, the second lens element, and the third lenselement along the optical axis.
 5. The ocular optical system accordingto claim 1, wherein the ocular optical system further satisfies:0.7≤AAG/T2≤25, where AGG is a sum of two air gaps from the first lenselement to the third lens element along the optical axis, and T2 is athickness of the second lens element along the optical axis.
 6. Theocular optical system according to claim 1, wherein the ocular opticalsystem further satisfies: 2.5≤250 mm/EFL≤25, where EFL is an effectivefocal length of the ocular optical system.
 7. The ocular optical systemaccording to claim 1, wherein the ocular optical system furthersatisfies: 1≤ALT/ER≤10, where ALT is a sum of thicknesses of the firstlens element, the second lens element, and the third lens element alongthe optical axis, and ER is a distance from a pupil of the eye of theobserver to the first lens element along the optical axis.
 8. An ocularoptical system, for imaging of imaging rays entering an eye of anobserver via the ocular optical system from a display screen, a sidefacing towards the eye being an eye-side, a side facing towards thedisplay screen being a display-side, the ocular optical systemcomprising a first lens element, a second lens element, and a third lenselement from the eye-side to the display-side in order along an opticalaxis, the first lens element, the second lens element, and the thirdlens element each comprising an eye-side surface and a display-sidesurface; the first lens element having refracting power; thedisplay-side surface of the second lens element having a convex portionin a vicinity of a periphery of the second lens element; and thedisplay-side surface of the third lens element having a concave portionin a vicinity of the optical axis, the third lens element havingrefracting power, wherein lens elements of the ocular optical systemhaving refracting power are only the first lens element, the second lenselement, and the third lens element, and the ocular optical systemsatisfies:T3/G23≤4.3; andG3D/T3≤3.51, where T3 is a thickness of the third lens element along theoptical axis, G23 is an air gap from the second lens element to thethird lens element along the optical axis, and G3D is a distance fromthe third lens element to the display screen along the optical axis. 9.The ocular optical system according to claim 8, wherein the ocularoptical system further satisfies: ER/T3≤4.31, where ER is a distancefrom a pupil of the eye of the observer to the first lens element alongthe optical axis.
 10. The ocular optical system according to claim 8,wherein the ocular optical system further satisfies: 0.5≤T1/T2≤10, whereT1 is a thickness of the first lens element along the optical axis, andT2 is a thickness of the second lens element along the optical axis. 11.The ocular optical system according to claim 8, wherein the ocularoptical system further satisfies: EFL/AAG≤6.2, where EFL is an effectivefocal length of the ocular optical system, and AGG is a sum of two airgaps from the first lens element to the third lens element along theoptical axis.
 12. The ocular optical system according to claim 8,wherein the ocular optical system further satisfies: 3≤SL/ER≤29, whereSL is a distance from a pupil of the eye of the observer to the displayscreen along the optical axis, and ER is a distance from a pupil of theeye of the observer to the first lens element along the optical axis.13. The ocular optical system according to claim 8, wherein the ocularoptical system further satisfies: (ER+G12+G3D)/T3≤8.01, where ER is adistance from a pupil of the eye of the observer to the first lenselement along the optical axis, and G12 is an air gap from the firstlens element to the second lens element along the optical axis.
 14. Theocular optical system according to claim 8, wherein the ocular opticalsystem further satisfies: 2.2≤ALT/T2≤50, where ALT is a sum ofthicknesses of the first lens element, the second lens element, and thethird lens element along the optical axis, and T2 is a thickness of thesecond lens element along the optical axis.
 15. An ocular opticalsystem, for imaging of imaging rays entering an eye of an observer viathe ocular optical system from a display screen, a side facing towardsthe eye being an eye-side, a side facing towards the display screenbeing a display-side, the ocular optical system comprising a first lenselement, a second lens element, and a third lens element from theeye-side to the display-side in order along an optical axis, the firstlens element, the second lens element, and the third lens element eachcomprising an eye-side surface and a display-side surface; the firstlens element having refracting power; the eye-side surface of the secondlens element having a convex portion in a vicinity of the optical axis;and the display-side surface of the third lens element having a concaveportion in a vicinity of the optical axis, the eye-side surface of thethird lens element having a concave portion in a vicinity of a peripheryof the third lens element, wherein lens elements of the ocular opticalsystem having refracting power are only the first lens element, thesecond lens element, and the third lens element, and the ocular opticalsystem satisfies:T3/G23≤4.3; andG3D/T3≤3.51 where T3 is a thickness of the third lens element along theoptical axis, G23 is an air gap from the second lens element to thethird lens element along the optical axis, and G3D is a distance fromthe third lens element to the display screen along the optical axis. 16.The ocular optical system according to claim 15, wherein the ocularoptical system further satisfies: ER/G23≤20, where ER is a distance froma pupil of the eye of the observer to the first lens element along theoptical axis.
 17. The ocular optical system according to claim 15,wherein the ocular optical system further satisfies: 0.7≤T1/T3≤10, whereT1 is a thickness of the first lens element along the optical axis. 18.The ocular optical system according to claim 15, wherein the ocularoptical system further satisfies: 1.23≤TTL/EFL≤10, where TTL is adistance from the eye-side surface of the first lens element to thedisplay screen along the optical axis, and EFL is an effective focallength of the ocular optical system.
 19. The ocular optical systemaccording to claim 15, wherein the ocular optical system furthersatisfies: 0.4≤AAG/G3D≤0.20, where AGG is a sum of two air gaps from thefirst lens element to the third lens element along the optical axis. 20.The ocular optical system according to claim 15, wherein the ocularoptical system further satisfies: (ER+G12+G3D)/G23≤36, where ER is adistance from a pupil of the eye of the observer to the first lenselement along the optical axis, and G12 is an air gap from the firstlens element to the second lens element along the optical axis.